Can I still sync to iTunes with my iPhone 4?

Okay I have an iPhone 4 with IOS 7.1.2 and iTunes 12.3.2 and though it shows the music on my phone when I open iTunes it doesn't show an option to sync when I click on file and devices it shows sync but its gray and doesn't do anything though when it shows the songs on my iPhone. Is there anything I can do?

I would ensure that you're on the latest version of iTunes. If you are, I would uninstall and reinstall iTunes to ensure that the device drivers for the iPhone are installed onto your computer. Usually when the sync button is grayed out, it means that iTunes can't see your device. And yes, the latest version of iTunes should be able to work just fine with the iPhone 4.